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Prove that: ((64)/(125))^(-2/3)+1/(((256...

Prove that: `((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/(root(3)64))=(65)/(16)`

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Factorize: (64)/(125)x^3-8-(96)/(25)x^2+(48)/5x\

Simplify : ((8)/(27))^(-1//3)xx((25)/(4))^(1//2)xx((4)/(9))^(0)+((125)/(64))^(1//3)

Prove that: sin^-1(3/5)-cos^-1(12/13)=sin^-1(16/65)

Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

Prove that: sin^(-1)(4/5)+sin^(-1)(5/(13))+sin^(-1)((16)/(65))=pi/2

solve: (64)^(1/2)

Evaluate : 5^(-4)xx(125)^((5)/(3))+(25)^(-(1)/(2))

sqrt(2^x(4^x(0. 125)^(1/ x))^(1/3))=4.(2^(1/3))

Evaluate each of the following by removing radical signs and negative indices wherever they occur: (i)\ (64)^(1/3) (ii) (125)^(-1/3) (iii)\ (27)^(-2/3) (iv) ((64)/(25))^(-3/2)

simplify (i) (1^(3)+2^(3)+3^(3))^(1/2) (ii) (3/5)^(4)(8/5)^(-12)(32/5)^(6) ,(iii) (1/27)^(-2/3) (vi) [((625)^(-1/2)))^(-1/4)]^(2) ,(v) (9^(1/3)xx27^(-1/2))/(3^(1/6)xx3^(-2/3)) (vi) 64^(-1/3)[64^(1/3)-64^(2/3)] (8^(1/3)xx16^(1/3))/(32^(-1/3)

RD SHARMA ENGLISH-EXPONENTS OF REAL NUMBER-All Questions
  1. Prove that: (2^(1/2)\ xx\ 3^(1/3)\ xx\ 4^(1/4))/(10^(-1/5)\ xx\ 5^(3/5...

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  2. Prove that: (i)\ sqrt(1/4)+\ (0. 01)^(-1/2)-\ (27)^(2/3)=3/2 (ii)\...

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  3. Prove that: ((64)/(125))^(-2/3)+1/(((256)/(625))^(1/4))+\ ((sqrt(25))/...

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  4. Prove that: (3^(-3)\ xx\ 6^2xx\ sqrt(98))/(5^2\ xx\ root(3)(1/(25))\ x...

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  5. Prove that: ((0. 6)^0-\ (0. 1)^(-1))/((3/8)^(-1)\ (3/2)^3+\ (-1/3)^(-1...

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  6. Solve: 1/(1+x^(a-b))+1/(1+x^(b-a))=?

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  7. Show that : (x^(a(b-c)))/(x^(b(a-c)))÷((x^b)/(x^a))^c=1 ((x^(a+b))^2...

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  8. Solve the following equation - (i) 2^(x+1)=8

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  9. Show that: (i)\ (x^(a-b))^(a+b)\ (x^(b-c))^(b+c)\ (x^(c-a))^(c+a)=1 ...

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  10. Show that: ((a^(x+1))/(a^(y+1)))^(x+y)\ ((a^(y+2))/(a^(z+2)))^(y+z)\ (...

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  11. Show that: ((3^a)/(3^b))^(a+b)\ ((3^b)/(3^c))^(b+c)\ ((3^c)/(3^a))^(c+...

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  12. If 2^x = 3^y =12^z show that 1/z= 1/y+2/x

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  13. If 2^x=3^y=6^(-z) prove that 1/x+1/y+1/z=0

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  14. If a^x=b^y=c^z and b^2=a c , then show that y=(2z x)/(z+x)

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  15. If 3^x=5^y=(75)^z show that z=(xy)/(2x+y

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  16. If 27^x=9/(3^x), find xdot

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  17. Find the values of x in each of the following : (i)2^(5x)-:2^x=2^(20/...

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  18. Find the value of x in each of the following: (i)\ (3/5)^x\ (5/3)^(2x)...

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  19. Find the value of x in each of the following: 2^(x-7)\ xx\ 5^(x-4)=125...

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  20. Find the value of x in each of the following: (i)\ 5^(2x+3)=1 (ii)\ ...

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